Physics-based Modeling and Control of Homogeneous Charge Compression Ignition (HCCI) Engines

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Physics-based Modeling and Control of Homogeneous
Charge Compression Ignition (HCCI) Engines

• Gregory M. Shaver
• Dynamic Design Lab
• May 6th, 2005
• Department of Mechanical Engineering
• Stanford University

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Outline

• What is residual-affected HCCI? What are its
  benefits?
• Hurdles to practically implementing HCCI
• Lack of combustion trigger
• Cyclic coupling
• Dynamic modeling of HCCI
• Making HCCI practical with feedback control
• Conclusions and future work

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What is Residual-Affected HCCI?

• Residual-Affected Homogeneous Charge Compression
  Ignition
• Advanced combustion strategy for piston engines
• Combustion due to uniform auto-ignition using
  compression alone
• Hot exhaust gases reinducted using Variable Valve
  Actuation (VVA)
• Main benefits
• Increased efficiency compared to SI
• Modest compression ratios
• Drastic reduction in NOx emissions (i.e. smog)

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HCCI with Variable Valve Actuation
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HCCI with Variable Valve Actuation

• Reactants (fuel air) previously exhausted
  gases (residual) inducted

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HCCI with Variable Valve Actuation

• Reactants (fuel air) previously exhausted
  gases (residual) inducted
• Compression of mixture

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HCCI with Variable Valve Actuation

• Reactants (fuel air) previously exhausted
  gases (residual) inducted
• Compression of mixture causes auto-ignition
• uniform, fast uncontrolled

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HCCI with Variable Valve Actuation

• Reactants (fuel air) previously exhausted
  gases (residual) inducted
• Compression of mixture causes auto-ignition
• uniform, fast uncontrolled
• Useful work from expansion

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HCCI with Variable Valve Actuation

• Reactants (fuel air) previously exhausted
  gases (residual) inducted
• Compression of mixture causes auto-ignition
• uniform, fast uncontrolled
• Useful work from expansion
• Hot combustion products exhausted

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HCCI with Variable Valve Actuation

• Reactants (fuel air) previously exhausted
  gases (residual) inducted
• Compression of mixture causes auto-ignition
• uniform, fast uncontrolled
• Useful work from expansion
• Hot combustion products exhausted, portion
  reinducted

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HCCI with Variable Valve Actuation

• Valve motions from VVA determine
• inducted gas composition
• amount of compression

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HCCI with Variable Valve Actuation
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HCCI with Variable Valve Actuation

• Sudden rise in pressure combustion
  initiation

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HCCI with Variable Valve Actuation

• Sudden rise in pressure combustion
  initiation
• Work output

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HCCI with VVA -Challenges

• Goal achieve desired combustion timing work
  output
• Challenges
• No direct initiator of combustion
• Cycle-to-cycle coupling through exhaust gas
• Significantly complicate transient load operation

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HCCI with VVA -Challenges

• Goal achieve desired combustion timing work
  output
• Challenges
• No direct initiator of combustion
• Cycle-to-cycle coupling through exhaust gas
• Significantly complicate transient load operation
• To date HCCI impractical!!

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Research Goals

• Make HCCI practical through closed-loop control
• Stabilize process control work output
• Modeling Objective Simple physical models that
  capture behavior most relevant for control
• Cyclic coupling
• Combustion timing
• In-cylinder pressure evolution (work output)
• Control Objective - Control of
• Combustion timing make combustion sure happens!
• Work output the key output of the engine
• efficiency reduced emissions come as result of
  process

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Previous Work Simulation Modeling

• Ogink and Golovitchev 2002, Babajimopoulos et al.
  2002
• Multi-zone modeling of HCCI
• Kong et al. 2002
• Multi-dimensional CFD models using detailed
  chemistry
• Many others
• Complex flow and chemical kinetics models
• Capture general steady state behavior
• Ignore cycle-to-cycle coupling
• Exhibit long run times - 12 hours per engine
  cycle

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Contributions Simulation Modeling

• Developed a simulation model of residual-affected
  HCCI that
• Captures the cyclic coupling
• Predicts behavior during steady state
  transients
• Captures ignition via kinetics with a simple,
  intuitive model
• runtimes 15 seconds per engine cycle (amenable
  to use as a control testbed)

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Previous Work - Control

• Agrell et al. 2003, Haraldsson et al. 2003,
  Bengtsson et al. 2004, Olsson et al. 2001,
  Matthews et al. 2005, others
• Various approaches to control combustion timing
  or work output
• In all cases controller hand-tuned or
  synthesized from black-box models

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Contributions - Control

• Physics-based control model of HCCI
• The first physics-based approach to control of
  HCCI
• Generalizable
• Enables use of control engineering tools
• Theoretical control design
• Stability analysis
• Control strategies for
• Combustion timing
• Peak pressure or work output

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Outline - Modeling Strategies

• Simulation model
• Gain some intuition of the process
• What are key features?
• What are relevant control inputs outputs?
• Control model
• Need a slightly simpler physical description for
  synthesis
• The launching point for developing control
  strategies
• ..making HCCI practical!!

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Experimental Apparatus

• Single cylinder engine
• With VVA
• Fuel used Propane
• Compression ratio
• Variable 13-15.5
• Engine speed
• Fixed 1800 rpm
• In-cylinder pressure transducer
• Combustion timing
• Peak pressure
• Work output

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HCCI Simulation Model

• 1st law analysis of cylinder and exhaust manifold

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HCCI Simulation Model

• 1st law analysis of cylinder and exhaust manifold
• Steady state 1D compressible flow relations

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HCCI Simulation Model

• 1st law analysis of cylinder and exhaust manifold
• Steady state 1D compressible flow relations
• Heat transfer
• In-cylinder (modified Woschni)
• Ref Chang et al. 2004
• Exhaust manifold

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HCCI Simulation Model

• 1st law analysis of cylinder and exhaust manifold
• Steady state 1D compressible flow relations
• Heat transfer
• In-cylinder (modified Woschni)
• Ref Chang et al. 2004
• Exhaust manifold
• Combustion model
• Wiebe function
• What do we use as a combustion trigger?

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HCCI Simulation Model

• 1st law analysis of cylinder and exhaust manifold
• Steady state 1D compressible flow relations
• Heat transfer
• In-cylinder (modified Woschni)
• Ref Chang et al. 2004
• Exhaust manifold
• Combustion model
• Wiebe function
• What do we use as a combustion trigger?
• Resulting Model 9 nonlinear ODEs

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Temperature Threshold

• Assume HCCI occurs at a threshold temperature
• A fit at one temperature

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Temperature Threshold

• Assume HCCI occurs at a threshold temperature
• Fit at one temperature doesnt hold at others!

Increasing residual
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What Happened?

• Simulation model earlier timing for increasing
  residual
• More residual means mixture temperature
• Higher temperature leads to early timing
• Experiments show more constant timing
• Is some physical effect missing?
• Yes! Concentration of reactants
• More residual means lower reactant concentration

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Integrated Arrhenius Rate Equation

• Simple model for start of combustion
• Integrated Arrhenius rate
• Constant threshold,
• a, b and Ea from published experiments
• Contributions from temperature reactant
  concentration captured

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Integrated Arrhenius Rate

• Set threshold at one operating point

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Integrated Arrhenius Rate

• Set threshold at one operating point and
  pressure, timing work output at all points is
  captured

Increasing residual
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Integrated Arrhenius Rate

• Note can vary composition without much change in
  timing

Increasing residual
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Simulation Model Can it be extended?

• Steady state behavior with propane captured
• What about transients?
• Changes in load
• Can the model capture these?

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Simulation Model Transients

• 1st operating point has higher steady state
  temperature than 2nd
• The elevated exhaust temperature advances
  combustion process during transition
• As exhaust temperature decreases, behavior
  reaches new steady state

Experiment
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Simulation Model Transients
Experiment

• Simple model captures the coupling and ignition
  behavior during transition

Simulation
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Results from Simulation modeling

• Aspects most relevant for control captured with
  simple simulation model
• Cyclic coupling combustion timing
• In-cylinder pressure evolution
• Approach can handle
• Steady-state behavior
• Transients
• A valuable virtual testbed for control

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Motivation for Control Model

• Simulation model has a lot of benefits
• Still, too complex for synthesizing control
  strategies
• Motivates a simpler dynamic model
• Enabled through additional physical assumptions
• Discretizing the process (induction, compression,
  etc.)
• Linking processes

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Control Model Assumptions

• Assumptions
• Induction atmospheric pressure
• Isentropic compression expansion
• HCCI is fast constant volume combustion
• In-cylinder heat transfer of combustion energy

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Control Model Assumptions
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A Simple Control Model
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A Simple Control Model

• Step through process to develop model of dynamics

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A Simple Control Model

• Step through process to develop model of dynamics

dynamics
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Peak Pressure Dynamics

• The peak pressure dynamics takes the form
• Fairly complex nonlinear dynamic model

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Peak Pressure Dynamics

• The peak pressure dynamics takes the form
• Fairly complex nonlinear dynamic model
• Can see dependence on
• Control inputs

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Peak Pressure Dynamics

• The peak pressure dynamics takes the form
• Fairly complex nonlinear dynamic model
• Can see dependence on
• Control inputs
• Cyclic coupling

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Peak Pressure Dynamics

• The peak pressure dynamics takes the form
• Fairly complex nonlinear dynamic model
• Can see dependence on
• Control inputs
• Cyclic coupling
• Combustion timing

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Peak Pressure Dynamics

• The peak pressure dynamics takes the form
• Fairly complex nonlinear dynamic model
• Can see dependence on
• Control inputs
• Cyclic coupling
• Combustion timing
• How do we model initiation of combustion, qcomb?

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model
• Integrand takes on largest value at TDC

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model
• Integrand takes on largest value at TDC
• Simplify begin integration at TDC with values at
  TDC

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model
• Integrand takes on largest value at TDC
• Simplify begin integration at TDC with values at
  TDC

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model
• Integrand takes on largest value at TDC
• Simplify begin integration at TDC with values at
  TDC

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model
• Integrand takes on largest value at TDC
• Simplify begin integration at TDC with values at
  TDC
• Algebraic expression exists for each variable

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Combustion Timing Dynamics

• Recall the integrated Arrhenius rate model
• Integrand takes on largest value at TDC
• Simplify begin integration at TDC with values at
  TDC
• Algebraic expression exists for each variable

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Control Model

• Peak pressure and combustion timing dynamics
  together give
• A nonlinear 2-state, dynamic, discrete system
  model

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Control Model Validation

• Control model captures
• Steady state transient
• Peak pressure
• Combustion Timing
• Captures
• Cyclic coupling
• Ignition via kinetics

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Control Modeling Summary

• HCCI is difficult to control
• Cyclic coupling
• No direct combustion trigger
• Control model captures these phenomena!!
• Simple model tells us how dynamics are affected
  by control inputs
• Is a launching point for
• Synthesizing control strategies
• Assessing system stability
• Generalizable

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Outline of Control Implementations

• From control model
• Peak-pressure control at constant combustion
  timing
• Work output control at constant combustion timing
• Simultaneous peak pressure and combustion timing
  control
• Many other approaches possible

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Peak Pressure Control w/ Constant timing

• Fix final valve closure
• Vary composition to control peak pressure
• A static approach to controlling timing
• A large number of control approaches can be
  utilized

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Peak Pressure Control w/ Constant timing Linear
Controller Synthesis

• A common control approach is to linearize the
  system model
• Linearizing about an operating point
  yields
• Simple linear control laws can be synthesized

where
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Peak Pressure Control w/ Constant timing

• In closed-loop
• Controller synthesized from linearized version of
  model
• Is controller stable in closed-loop with
  nonlinear model?

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Peak Pressure Control w/ Constant timing
Nonlinear Stability Analysis

• Using
• Lyapunov stability theory
• Convex optimization
• Shows
• Simple linear controller stabilizes entire
  operating regime

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Peak Pressure Control w/ Constant timing
Experimental Implementation

• Accurate control of peak pressure
• Mean tracking
• Fluctuation reduction
• Increases robustness
• Little change in phase
• What about direct control of work output (IMEP)?

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Experimental Work Output Control

• Rapid mean tracking fluctuation reduction
• We can control work output, while keeping timing
  roughly constant

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Experimental Work Output Control

• Positive and negative load transients
• What about simultaneous control of combustion
  timing and work output?

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Combustion Timing Work Output Control

• Add other control input final valve closure
• Significant control knob for combustion timing
• Simple approach
• Separate linear controllers for peak pressure and
  timing

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Decoupled Peak Pressure and Phase Control

• Maintain cycle-to-cycle peak pressure controller,
  vary phase more slowly

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Experiments with Decoupled Control

• Approach works
• Simultaneous control of
• timing and peak pressure

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Comments on Control Experiments

• Simple physics-based controllers works well
• Implementation is straightforward
• Mean tracking fluctuation reduction of
• peak pressure
• work output
• Combustion timing fairly constant
• Independent control of peak pressure combustion
  timing
• Many others possible

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Conclusion

• HCCI has a promising future as a cleaner, more
  efficient strategy
• Hurdle controlling the process
• No combustion initiator cycle-to-cycle coupling
• The good news HCCI is amenable to model-based
  control
• Key behaviors captured in both simulation and
  control models
• Simulation control models capture
• Steady-state
• Transients
• Physics-based control of
• Peak pressure
• Work output
• Combustion timing

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Future Work

• Study different control approaches
• Control of multi-cylinder HCCI engines
• Results to date with single-cylinder engines
• Cylinder-to-cylinder dynamics now play a key
  role!
• Change the world!

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Acknowledgments

• Chris Gerdes
• The Dynamic Design Lab
• Partners in crime
• Matt Roelle Nikhil Ravi
• A great sponsor Robert Bosch Corporation
• Jean-Pierre Hathout, Jasim Ahmed, Aleks Kojic
  Sungbae Park
• The defense Committee
• Chris Edwards, Sanjay Lall, Matt Franchek Steve
  Rock
• Stanford University